1. Field of Invention
The present invention relates to a non-linearity compensation circuit and a bandgap reference circuit using the same, and more particularly, to a non-linearity compensation circuit capable of improving the precision of a bandgap reference voltage and a bandgap reference circuit using the same.
2. Description of Related Art
Digital-to-analog converters (DACs), analog-to-digital converters (ADCs) or regulators need at least one fixed and stable reference voltage. It is preferred that the reference voltage is stably regenerated each time the power source is started. An ideal reference voltage even had better not be influenced by processing differences, changes in the operating temperature, and power source variations.
A bandgap reference circuit can be used to provide the reference voltage. Therefore, bandgap reference circuits play an important role in many electronic systems as they may determine the stability and precision of the entire systems.
FIG. 1 shows a circuit diagram of a conventional bandgap reference circuit. As shown in FIG. 1, the conventional bandgap reference circuit 100 comprises a current mirror composed of metal-oxide-semiconductor (MOS) transistors M101˜M103, operation amplifiers OP101˜OP103, resistors R101, R102, R103A and R103B, and two bipolar junction transistors (BJT) B101˜B102. The connection of various elements can be understood from FIG. 1. The resistors R103A and R103B have the same resistance.
The reference voltage VBG1 can be represented by the following equations.VBG1=0.5*(VNTC1+VPTC1)=0.5*(VBE1A+VPTC1)=0.5*(VBE1A+K1*VT)  (1)VPTC1=IPTAT1*R102=(ΔVBE/R101)*R102  (2)ΔVBE=VT*ln(n)  (3)wherein, VT represents the thermal voltage (the value is KT/q, wherein K is the Boltzmann's constant=1.28×10−23 Joules/Kelvin, T is the absolute temperature, q=1.602×10−29 Coulomb), K1 is a constant, VBE1A represents the base-emitter voltage of the BJT transistor B101, VNTC1 represents a negative temperature coefficient (NTC) voltage, VPTC1 represents a proportional to absolute temperature (PTAT) voltage, IPTAT1 is a PTAT current, and n is the size ratio of the transistor B102 to the transistor B101.
The base-emitter voltage VBE of the BJT transistors can be represented by the following equation.VBE=VG0−(VG0−VBE0)*T/T0−(η−α)*VTln(T/T0)  (4)
In equation (4), T0 represents the reference voltage, T represents the operating temperature, VBE0 represents the base-emitter voltage obtained at the reference temperature T0, VG0 is the silicon bandgap voltage at the absolute temperature of 0, η is the structural coefficient of the BJT transistors (the value is between 2 and 6), and the coefficient α is determined by the type of the biasing current of the BJT transistors. When the biasing current is a PTAT current, α=1, and when the biasing current is a temperature independent current, α=0.
As the biasing current of the transistors B101 and B102 is equal to the PTAT current, α=1. Therefore, the base-emitter voltages VBE1A and VBE1B of the transistors B101 and B102 can be respectively represented by the following equations.VBE1A=VG0−(VG0−VBE0)*T/T0−(η−1)*VTln(T/T0)  (5)VBE1B=VG0−(VG0−VBE0)*T/T0−(η−1)*VTln(T/T0)  (6)
Introduce equations (2)˜(6) into equation (1), the following equation is obtained.
                              V                      BG            ⁢                                                  ⁢            1                          =                              1            2                    ×                      {                                          [                                                      V                                          BG                      ⁢                                                                                          ⁢                      0                                                        -                                                            (                                                                        V                                                      BG                            ⁢                                                                                                                  ⁢                            0                                                                          -                                                  V                                                      BE                            ⁢                                                                                                                  ⁢                            0                                                                                              )                                        ⁢                                          T                                              T                        0                                                                              -                                                            (                                              η                        -                        1                                            )                                        ⁢                                          V                      T                                        ⁢                    ln                    ⁢                                          T                                              T                        0                                                                                            ]                            +                              [                                                                            R                      ⁢                                                                                          ⁢                      102                                                              R                      ⁢                                                                                          ⁢                      101                                                        ·                                      V                    T                                    ·                                      ln                    ⁡                                          (                      n                      )                                                                      ]                                      }                                              (        7        )            
In equation (7), if K2=R102/R101*ln(n), K2*VT can be used to compensate the linear term in VBE. (η−1)*VTln(T/T0) (or VTln(T/T0)) is a non-linear term in VBE. Therefore, the compensation effect of the reference voltage VBG1 is limited, and the non-linearity effect still exists.
FIG. 2 shows a concept diagram of compensation of the conventional bandgap reference circuit. FIG. 2 shows that the reference voltage VBG is the sum of K2*VT (proportional to absolute temperature) and VBE (negative temperature dependent). However, in the conventional bandgap reference circuit, VBE has a non-linearity effect. If the non-linearity effect of VBE is not well compensated, the characteristic diagram of the reference diagram presents a curve (non-ideal) phenomenon in the range of operating temperature, as shown in FIG. 3.
FIG. 3 shows that an ideal reference voltage VBG must remain stable in the range of operating temperatures, and be approximately 1.205V. The ideal VBE also must have a fine linear effect. However, the actual VBE has a non-linearity effect.
Therefore, the reference voltage resulting from adding the non-linear VBE and the linear K2*VT also presents the non-linear effect. Thus, the actual reference voltage exhibits quite a large difference in operating temperature range.
FIG. 4 shows a characteristic diagram of reference voltage VGB-temperature of the conventional art under different power source VDD (10.V˜1.5V) when the operating temperature is between −40° C. and 125° C., wherein curves A1˜E1 represent the variation curves of VGB when VDD=1.5V, VDD=1.4V, VDD=1.3V, VDD=1.2V, and VDD=1.1V respectively.
It can be seen from FIG. 4 that the reference voltage obtained in the conventional art still varies much as the conventional art cannot compensate the non-linear term in the reference voltage.
Therefore, a bandgap reference circuit for obtaining a stable reference voltage that does not vary much by compensating the non-linear term is needed.